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Minimax principle on energy dissipation of incompressible shear flow 被引量:1

Minimax principle on energy dissipation of incompressible shear flow
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摘要 The energy dissipation rate is an important concept in the theory of turbulence. Doering-Constantin's variational principle characterizes the upper bounds (maxi- mum) of the time-averaged rate of viscous energy dissipation. In the present study, an optimization theoretical point of view was adopted to recast Doering-Constantin's formu- lation into a minimax principle for the energy dissipation of an incompressible shear flow. Then, the Kakutani minimax theorem in the game theory is applied to obtain a set of conditions, under which the maximization and the minimization in the minimax principle are commutative. The results explain the spectral constraint of Doering-Constantin, and confirm the equivalence between Doering-Constantin's variational principle and Howard- Busse's statistical turbulence theory. The energy dissipation rate is an important concept in the theory of turbulence. Doering-Constantin's variational principle characterizes the upper bounds (maxi- mum) of the time-averaged rate of viscous energy dissipation. In the present study, an optimization theoretical point of view was adopted to recast Doering-Constantin's formu- lation into a minimax principle for the energy dissipation of an incompressible shear flow. Then, the Kakutani minimax theorem in the game theory is applied to obtain a set of conditions, under which the maximization and the minimization in the minimax principle are commutative. The results explain the spectral constraint of Doering-Constantin, and confirm the equivalence between Doering-Constantin's variational principle and Howard- Busse's statistical turbulence theory.
出处 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第7期805-814,共10页 应用数学和力学(英文版)
基金 supported by the National Natural Science Foundation of China (No.10772103) the Shanghai Leading Academic Discipline Project (No.Y0103)
关键词 minimax theorem variational method dissipation rate upper bound game theory turbulence minimax theorem, variational method, dissipation rate, upper bound game theory, turbulence,
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